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A problem in additive number theory

  • Jörg Brüdern (a1)

The determination of the minimal s such that all large natural numbers n admit a representation as

is an interesting problem in the additive theory of numbers and has a considerable literature, For historical comments the reader is referred to the author's paper [2] where the best currently known result is proved. The purpose here is a further improvement.

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[1]Brüdern J.. Sums of squares and higher powers. J. London Math. Soc. (2) 35 (1987), 233243.
[2]Brüdern J.. Sums of squares and higher powers. II. J. London Math. Soc. (2) 35 (1987), 244250.
[3]Hardy G. H. and Wright E. M.. An Introduction to the Theory of Numbers, 5th edn. (Oxford University Press, 1979).
[4]Thanigasalam K.. On sums of powers and a related problem. Acta Arith. 36 (1980), 125141.
[5]Vaughan R. C.. The Hardy–Littlewood Method (Cambridge University Press, 1981).
[6]Vaughan R. C.. Some remarks on Weyl sums. In Topics in Classical Number Theory, Colloq. Math. Soc. Janos Bolyai 34 (Elsevier North-Holland, 1984), 15851602.
[7]Vaughan R. C.. On Waring's problem for smaller exponents. Proc. London Math. Soc. (3) 52 (1986), 445465.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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